Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays

TL;DR

This paper explores flatband ferromagnetism in the Hubbard model, presenting a general theorem, unusual particle occupation behavior, and specific ferromagnetic patterns in small quantum dot arrays, which are experimentally testable.

Contribution

It introduces a geometry-independent theorem on flatband ferromagnetism, highlights unexpected occupation patterns, and identifies ferromagnetic states in small quantum dot arrays.

Findings

Theorem on conditions for flatband ferromagnetism and degeneracy.

Unusual particle occupation behavior contradicting intuition.

Ferromagnetic patterns in small pentagonal and hexagonal plaquettes.

Abstract

We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagnetism which appears in small pentagonal and hexagonal plaquettes at filling factors of roughly 3/10 and 1/4. These examples require only a small number of lattice sites, and may be observable in quantum dot arrays currently available as laboratory spin qubit arrays.